There is no known number that is bigger than Graham’s number.
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Graham’s number is an enormous number, used in the field of mathematics. The number is so large that it is impossible to even write it down in full, as it has more digits than the observable universe. The number was discovered in 1971 by mathematician Ronald Graham and is a solution to a problem in the field of Ramsey theory.
“There’s a certain liberating quality in realizing how small you are, and how far you are from knowing everything.” – Ronald Graham
Here are some interesting facts about Graham’s number:
- Graham’s number is so large that even if every digit of it were written on particles known as Planck spheres, the resulting mass would collapse into a black hole due to its size.
- The number is named after Ronald Graham, who discovered it while working on a mathematical problem related to Ramsey theory. In recognition of his work, it was named Graham’s number.
- The number is a theoretical construct and has no practical application in everyday life but is of great importance in the field of mathematics.
- It is an upper bound to the solution of a problem in Ramsey theory called the Graham’s problem. The problem deals with the minimum number of colors necessary to color the nodes of a particular type of hypercube.
- The number has 87 digits in its smallest form, with each digit being a 3.
- The specific value of Graham’s number is not known. However, it has been calculated that it is larger than 7.5 x 10^365.
- “Graham’s number is so large that the observable universe is not big enough to contain an ordinary digital representation of it.” – Carl Sagan
Here is a table showing some other large numbers in comparison to Graham’s number:
| Number | Digits |
|---|---|
| Graham’s number | Over 87 |
| Skewes’ number | 39 |
| One hundred | 3 |
| One hundred thousand | 6 |
| One million | 7 |
| One billion | 9 |
| Googol | 100 |
| Googolplex | 10^100 |
| TREE(3) | Larger than Graham’s |
| Number googolplexian | 10^10^100 |
I discovered more solutions online
The number after Graham’s Number is called a “Forcal” or G(1,000,000), while Graham’s Number is G(64). After Forcal you have a number called “Force Forcal”.
The Graham number is a very large number that has been used in mathematics to solve extremal problems. While mathematicians have attempted to develop solutions larger than the Graham number, none have been successful so far. Therefore, it can be said that nothing is currently bigger than the Graham number. Any number larger than the Graham number cannot be proven as a valid solution for an extremal problem. There is a number called Tier (n) that is larger than Graham’s number, but it is not considered a valid solution for an extremal problem.
While mathematicians have attempted to develop solutions larger than the Graham number, none have been successful so far. Therefore, it can be said that nothing is currently bigger than the Graham number. Furthermore, any number larger than the Graham number cannot be proven as a valid solution for an extremal problem.
I’ll give you a number to beat Graham’s number: Let Tier (n) = n raised to itself n times (n tiers) Examples: Tier (2) = Tier (3) = 3^ (3^3)
Video answer
The video discusses two number sequences: the TREE(n) and g(n), which can be extended into unimaginably large numbers, and the comparison between the growth rates of the two sequences. The speaker introduces the concept of fast-growing hierarchies, using sequences like successor, multiplication, exponentiation, and tetration, to measure the growth rates of the sequences. They then introduce a function, f_omega, which grows more quickly than any function that came before it and explain how to define ordinal numbers using Omega plus 1, Omega plus 2, and so on until reaching Omega times 3. The hierarchy includes Epsilon, Eta, and Veblen hierarchies, leading up to the Feferman-Schütte ordinal, gamma 0. The function f(gamma0) grows incredibly fast but cannot keep pace with the TREE sequence, which is even faster. The speaker concludes that TREE of Graham’s number is larger than Graham of TREE.
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Also question is, Is a googolplex bigger than Grahams number?
The response is: (This might sound familiar, as Google was named after this number, though they got the spelling wrong.) Graham’s number is also bigger than a googolplex, which Milton initially defined as a 1, followed by writing zeroes until you get tired, but is now commonly accepted to be 10googol=10(10100).
Similar
Is Aleph null bigger than Graham’s number? Response: Aleph null is the largest.
How big is Rayo’s number?
As a response to this: Rayo’s number: The smallest number bigger than any number that can be named by an expression in the language of first order set-theory with less than a googol (10100) symbols.
In this regard, How many zeros are there in Graham’s number? The answer is: 100 zeros
It is a one followed by 100 zeros. (Fun fact: this number inspired the name of the search engine Google, but the company’s founders accidentally misspelled it when checking whether the web domain was still available. The rest is history.)
What is larger than Graham’s number? Answer will be: Almost every positive integer is larger than Graham’s number. Indeed, it’s incredibly easy to think of numbers which are larger: there are infinitely many to choose from, yet there are only finitely many which are smaller. Physics BSc. Author has 3.4K answers and 12M answer views Updated 3 y What is value of g1 in graham’s number?
Considering this, Is Graham’s number bigger than a googolplex? This is the beauty of Mathematics. Graham’s number is much larger than many other larger numbers such as Skewes’ number and Moser’s Number, both of which are in turn much larger than a googolplex. Is a graham the biggest number?
Likewise, What is the upper bound of Graham’s number? Graham’s number, G, G, is much larger than N: N: {f^ {64} (4)}, f 64(4), where { f (n)\;=\;3\uparrow ^ {n}3}. f (n) = 3 ↑n 3. This weaker upper bound for the problem, attributed to an unpublished work of Graham, was eventually published and named by Martin Gardner in Scientific American in November 1977.
Also Know, Why was Graham’s number used? Graham’s number was used by Graham in conversations with popular science writer Martin Gardner as a simplified explanation of the upper bounds of the problem he was working on. In 1977, Gardner described the number in Scientific American, introducing it to the general public.
What is larger than Graham’s number?
The reply will be: Almost every positive integer is larger than Graham’s number. Indeed, it’s incredibly easy to think of numbers which are larger: there are infinitely many to choose from, yet there are only finitely many which are smaller. Physics BSc. Author has 3.4K answers and 12M answer views Updated 3 y What is value of g1 in graham’s number?
Also Know, What is googolplexian compared to Graham’s number?
Googolplexian is nothing compared to Graham’s number since googlplexian is merely 10^10^10^100 while it is already dwarfed by the first iteration for Graham’s number (3 ↑↑↑↑ 3 = 3 ↑↑↑ 7,625,597,484,987)
Besides, What is the upper bound of Graham’s number? Graham’s number, G, G, is much larger than N: N: {f^ {64} (4)}, f 64(4), where { f (n)\\;=\\;3\\uparrow ^ {n}3}. f (n) = 3 ↑n 3. This weaker upper bound for the problem, attributed to an unpublished work of Graham, was eventually published and named by Martin Gardner in Scientific American in November 1977.
Additionally, What is a Grahams number growth rate?
The answer is: Forget about TREE (3), your number isn’t even bigger than G (65) which is Grahams number followed by G (64) number of arrows in between them. A grahams number growth rate is not more than fw+1 while there are not enough finite ordinals to represent growth rate of TREE (3).